Monopoly and perfect competition

Short run market clearing for perfect competition with 100’s of firms

One firm100’s of firms

Question: In the long run, with free entry and exit, what will be the minimum price reached in perfect competition?Monopoly and Price Descrimination SHOW WORK

The Monopolists market demand curve is given by the equation (This is an inverse demand curve)

Pd(Q) = 3000 – 5Q

Assume that a monopolist

sells a product with

a total cost function

  1. MC equation for this monopolist is

MC=:= 20Q

  1. TR equation for this monopolist is

TR=3000Q-5Q2

  1. MR equation for this monopolist is

MR=3000Q-10Q

  1. Find the profit maximizing output for this monopolist.

MR=MC 3000Q-10Q = 20Q  Q=100

Q = 100 is profit maximizing output.

  1. Now sketch the appropriate TR and TC curves.

Hint: start with the curves in Prob. 7. Find Q where MR = 0. That gives you the Q for maximum TR and then find the Q’s whereTR=0

  1. Graph the AC, MC, demand and MR curves.

The problem here calls for finding the minimum MC, AC and the Q for which MR =0 and where of course, MC=MR. Make sure the horizontal scale and the corresponding mins and max are the same for the two graphs.

MC has a minimum of zero.

ATC = 1200/Q+10Q

ATC=MC at minimum ATC, so

1200/Q+10Q = 20Q

30Q2 = 1200  Q2 = 400  Q = 20

  1. How much profit (or loss) is being earned.

Profit () = TR-TC at Q= 100 or

 = Qprofitmx*( ATRQ=100-ATCQ=100)

P = 2500 at Q = 100

ATC= 1200/Q+10Q = 120+1000= 1120

Average profit per unit at max = 1380

 = 100*(2500-1120)=100*1380=138.000

  1. Illustrate the above calculated (monopoly) profit on the top graph.

Yellow Box illustrate Profit as (AR-ATC)*Q

  1. Calculate and illustrate producer’s surplus & consumer surplus as the difference between the price and the choke price and start-up price

Producer’s surplus = 100*500+(100*2000)/2 = 150,000

Equals yellow and orange fill in bottom graph.

Consumer’s surplus = (100*500)/2= 25,000

Equals dark blue vertical stripes in bottom graph.

Comparison in Efficiency to Perfect Competition: GRAPH ON First PAGE

  1. Calculate the price quantity that arise under perfection competition with a Supply curve P=20Q
Ps(Q)=Pd(Q) 20Q=3000-5Q  25Q=3000  Q=120 P=2400
  1. Compare the consumer and producer surplus under monopoly versus marginal cost pricing. Calculate the deadweight loss due to monopoly and illustration on graph.

Under marginal cost pricing.

Producer’s surplus = 120*(2400-0)/2 = 144,000

Equals yellow and orange fill in bottom graph.

Consumer’s surplus =120*(3000-2400)/2= 36,000

Equals dark blue vertical stripes in bottom graph.

Total Surplus = 144,000 + 36 = 180,000

Under Monopoly (from above page).

Producer’s surplus+ Consumer’s surplus = Total

150,000 + 25,000 = 175,000

Deadweight loss.

Deadweight loss = 180,000 – 175,000 = 5,000

Equals bright blue triangle in bottom graph of previous page

Area triangle equals

= (2500-2400)*20/2+(2400-2000)*20/2 = 5000

Monopoly and Price Descrimination

  1. Perfectly Discriminating Monopolist: Suppose this monopolist is able to capture the entire consumer surplus for any unit of output bought by the consumer. That is, the monopolist knows the maximum price that each buyer is willing to pay.
  1. What is the “equilibrium price”, the monopolist’ profit and what is the deadweight loss to society as a whole.”? Show on upper right

Because the monopolist gets the maximum price the consumers are willing to pay for each unit, the marginal revenue curve become the demand curve.He never cuts prices for the goods already sold on the left. So he produces where MC=P on demand curve.

Same equilibrium price and quantity as in perfect competition.

Q = 120 P = 2400 Producer’s surplus is 180,00

Regulation:Regulation of natural monopolies is necessary because unregulated monopolies produce too little and cause a deadweight loss by using too few resources in this industry compared to others. Regulation of utilities and other natural monopolies, however, forceg them to earn only a risk-adjusted normal rate of return on invested capital. This results (in the simplest case) of price being set equal to average cost which includes a normal rate of profit.. The resulting price is below the marginal cost (usually) and as a result, too much quantity is demanded. See the graph below.

The price is set at about 2000 and the quantity goes up by about 80. It is “too much” in the sense that some of the buyers are not will to pay at least the real social cost for the additional units demanded, i.e., SMB < SMC. .

The deadweight loss of producing too much is the red area. It equal about88,000

80*(2400-2000)/2 + 80*(4000-2400)/2 = 88,000

  1. In the simple model of government regulationof natural monopolies, the government regulates the monopoly to allow a normal rate of return which as you remember is already included in AC to allow for the opportunity cost of capital.

13.1What is the “regulated price” and output under this policy. SHOW ON GRAPH

P= ATC3000-5Q =1200/Q+10Q

13.2 What are the social benefits and social costs of this “regulation”?

X. Extra Credit: Allocation production among multiple plants

. Imagine that Gillette has a monopoly in the market for razor blades in Mexico. The market demand curve for blades in Mexico is P=968-20Q

where P is the price of blades in cents and Q is the annual demand for blades expressed in millions.

Gillette has two plants in which it can produce razor blades for the Mexican market: one in Los Angeles, California, and one in Mexico City. In its L. A. plant, Gillette can produce any quantity of razors it wants at a marginal cost of 8 cents per blade. Letting Q1 and MC1 denote the output and the marginal cost at the L.A plant, we have

MC1(Q1) = 8

The Mexican plant has a marginal cost function given by

MC2(Q2) = 1 + 0.5 Q2

Find Gillette’s profit maximizing price and quantity of output for the Mexican market overall. How will Gillette allocate its production between its Mexican plant and its U. S Plant?